package LC;

/**
 * https://leetcode.com/problems/minimum-path-sum/description/
 * Given a m x n grid filled with non-negative numbers,
 * find a path from top left to bottom right
 * which minimizes the sum of all numbers along its path.
 */
public class LC_064_MinimumPathSum_DP {
    public static void main(String[] args) {
        int[][] a = new int[][]{
                {0, 0, 0, 0},
                {9, 1, 33, 2},
                {0, 0, 1, 0}
        };
        int sum = Solution.minPathSum(a);
        System.out.println(sum);
    }

    static class Solution {
        static int minPathSum(int[][] grid) {
            int m = grid.length;
            int n = grid[0].length;
            for (int i = 1; i < m; i++)
                grid[i][0] += grid[i - 1][0];
            for (int i = 1; i < n; i++)
                grid[0][i] += grid[0][i - 1];
            for (int i = 1; i < m; i++)
                for (int j = 1; j < n; j++)
                    grid[i][j] += Math.min(grid[i - 1][j], grid[i][j - 1]);
            return grid[m - 1][n - 1];
        }
    }
}
